Cost-driven framework for progressive compression of textured meshes

1. A method, comprising:

obtaining, by processing circuitry of a server computer configured to encode information related to a surface of a three-dimensional object, data representing an initial level of detail (LOD), the initial LOD including an initial mesh LOD and an initial texture image LOD, the initial mesh LOD including an initial triangular mesh and an initial texture atlas;

generating, by the processing circuitry, a plurality of LODs based on the initial LOD, each of the LODs of the plurality of LODs including a respective mesh LOD and a respective texture image LOD, a first texture image LOD of a first LOD of the plurality of LODs being a refinement of a second texture image LOD of a second LOD of the plurality of LODs; and

performing, by the processing circuitry, single-rate encoding operations on the respective mesh LODs of a sequence of LODs of the plurality of LODs to produce a sequence of single-rate encoded mesh LODs, the single-rate encoded mesh LODs, when combined with an encoding of corresponding texture image LODs, forming an efficient compression of the data that, upon decoding, enables a client computer to render the surface at a plurality of LODs.

2. The method as in claim 1 , further comprising:

performing a texture encoding operation on the respective texture image LODs of the sequence of LODs to produce encoded texture image LODs; and

combining the encoded texture image LODs with the single-rate encoded mesh LODs to produce a hybrid-encoded recovery bitstream.

3. The method as in claim 2 , wherein the texture encoding operation is a progressive encoding operation, and the encoded texture image LODs are progressive-encoded texture image LODs.

4. The method as in claim 2 , further comprising transmitting the hybrid-encoded recovery bitstream to the client computer, the client computer being configured to perform a decompress operation on the hybrid-encoded recovery bitstream to render the surface on a display connected to the client computer at a specified LOD.

5. The method as in claim 1 , wherein the first LOD includes a first mesh LOD, and the second LOD includes a second mesh LOD, the first mesh LOD including a first texture atlas, the second mesh LOD including a second texture atlas, and

wherein generating the plurality of LODs includes specifying the initial texture atlas such that the first texture atlas and the second texture atlas are compatible with the initial texture atlas.

6. The method as in claim 1 , wherein the first LOD includes a first mesh LOD, and the second LOD includes a second mesh LOD, the first mesh LOD including a first texture atlas, the second mesh LOD including a second texture atlas, and

wherein generating the plurality of LODs includes generating an abstraction of the initial mesh LOD, the abstraction including a set of edges that form a one-to-one correspondence with a set of seam edges of the initial mesh LOD.

7. The method as in claim 6 , wherein generating the abstraction includes specifying the abstraction.

8. The method as in claim 6 , wherein generating the abstraction includes performing a mesh decimation operation on the initial mesh LOD.

9. The method as in claim 8 , wherein performing the mesh decimation operation includes performing a full-edge collapse operation on the initial mesh LOD.

10. The method as in claim 6 , wherein generating the abstraction includes performing an optimal Delaunay triangulation operation on the initial mesh LOD.

11. The method as in claim 6 , wherein generating the abstraction includes performing a variational shape approximation on the initial mesh LOD.

12. The method as in claim 1 , wherein the method further comprises performing a LOD selection operation to produce the sequence of LODs, the LOD selection operation including optimizing a cost function of candidate sequences of mesh LODs.

13. The method as in claim 12 , wherein performing the LOD selection operation further includes, for each of a candidate sequence of a specified number of LODs, generating, as the cost function, a sum of costs per LOD improvement, where the cost of an LOD improvement is based on a product of an amount of bits used and a distortion of an improved LOD.

14. The method as in claim 12 , wherein performing the LOD selection operation further includes, for a first element of the plurality of LODs, removing the first element of the plurality of LODs in response to a distortion of the LOD of the first element being less than a distortion of the LOD of a second element and a bitrate of the LOD of the first element being less than the bitrate of the LOD of the second element.

15. The method as in claim 12 , wherein selecting the sequence of LODs includes generating a directed acyclic graph (DAG) that represents the plurality of LODs, each node of the DAG representing a LOD of the plurality of LODs.

16. The method as in claim 15 , wherein generating the DAG includes generating a cost for each edge of the DAG.

17. A computer program product comprising a nontransitory storage medium, the computer program product including code that, when executed by processing circuitry of a user device configured to encode information related to a surface of a three-dimensional object, causes the processing circuitry to perform a method, the method comprising:

obtaining data representing an initial level of detail (LOD), the initial LOD including an initial mesh LOD and an initial texture image LOD, the initial mesh LOD including an initial triangular mesh and an initial texture atlas;

generating a plurality of LODs based on the initial LOD, each of the LODs of the plurality of LODs including a respective mesh LOD and a respective texture image LOD, a first texture image LOD of a first LOD of the plurality of LODs being a refinement of a second texture image LOD of a second LOD of the plurality of LODs; and

performing single-rate encoding operations on the respective mesh LODs of a sequence of LODs of the plurality of LODs to produce a sequence of single-rate encoded mesh LODs, the single-rate encoded mesh LODs, when combined with an encoding of corresponding texture image LODs, forming an efficient compression of the data that, upon decoding, enables a user client computer to render the surface at a plurality of LODs.

18. The computer program product as in claim 17 , wherein the first LOD includes a first mesh LOD, and the second LOD includes a second mesh LOD, the first mesh LOD including a first texture atlas, the second mesh LOD including a second texture atlas, and

wherein generating the plurality of LODs includes specifying the initial texture atlas such that the first texture atlas and the second texture atlas are compatible with the initial texture atlas.

19. An electronic apparatus configured to encode information related to a surface of a three-dimensional object, the electronic apparatus comprising:

memory; and

controlling circuitry coupled to the memory, the controlling circuitry being configured to:

obtaining data representing an initial level of detail (LOD), the initial LOD including an initial mesh LOD and an initial texture image LOD, the initial mesh LOD including an initial triangular mesh and an initial texture atlas;

generating a plurality of LODs based on the initial LOD, each of the LODs of the plurality of LODs including a respective mesh LOD and a respective texture image LOD, a first texture image LOD of a first LOD of the plurality of LODs being a refinement of a second texture image LOD of a second LOD of the plurality of LODs; and

performing single-rate encoding operations on the respective mesh LODs of a sequence of LODs of the plurality of LODs to produce a sequence of single-rate encoded mesh LODs, the single-rate encoded mesh LODs, when combined with an encoding of corresponding texture image LODs, forming an efficient compression of the data that, upon decoding, enables a client computer to render the surface at a plurality of LODs.

20. The electronic apparatus as in claim 19 , wherein the controlling circuitry is further configured to perform a LOD selection operation to produce the sequence of LODs, the LOD selection operation including optimizing a cost function of candidate sequences of mesh LODs.